`[20^5 .5^10]/[100^5]`
`=[(4.5)^5 .5^10]/[(10^2)^5]`
`=[4^5 .5^5 .5^10]/[10^10]`
`=[(2^2)^5 .5^15]/[(2.5)^10]`
`=[2^10 .5^15]/[2^10 .5^10]`
`=5^5=3125`
\(\dfrac{20^5.5^{10}}{100^5}=\dfrac{20^5.5^5.5^5}{20^5.5^5}=5^5=3125\)
\(\dfrac{20^5\cdot5^{10}}{100^5}=\dfrac{20^5\cdot5^{10}}{20^5\cdot5^5}=\dfrac{5^{10}}{5^5}=5^5=3125\)
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\(=\dfrac{20^5.5^{10}}{\left(20.5\right)^5}\\ =\dfrac{20^5.5^{10}}{20^5.5^5}\\ =\dfrac{5^{10}}{5^5}=5^5=3125\)